7.3. The Graph Abstract Data Type¶

The graph abstract data type (ADT) is defined as follows:

• Graph() creates a new, empty graph.
• add_vertex(vert) adds an instance of Vertex to the graph.
• add_edge(from_vert, to_vert) Adds a new, directed edge to the graph that connects two vertices.
• add_edge(from_vert, to_vert) Adds a new, directed edge to the graph that connects two vertices.
• get_vertex(vertkey) finds the vertex in the graph named vertkey.
• get_vertices() returns the list of all vertices in the graph.
• in returns True for a statement of the form vertex in graph, if the given vertex is in the graph, False otherwise.

Beginning with the formal definition for a graph there are several ways we can implement the graph ADT in Python. We will see that there are trade-offs in using different representations to implement the ADT described above. There are two well-known implementations of a graph, the adjacency matrix and the adjacency list. We will explain both of these options, and then implement one as a Python class.